Problem: Simplify the following expression: $ z = \dfrac{4k + 4}{k + 9} - \dfrac{3}{10} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{4k + 4}{k + 9} \times \dfrac{10}{10} = \dfrac{40k + 40}{10k + 90} $ Multiply the second expression by $\dfrac{k + 9}{k + 9}$ $ \dfrac{3}{10} \times \dfrac{k + 9}{k + 9} = \dfrac{3k + 27}{10k + 90} $ Therefore $ z = \dfrac{40k + 40}{10k + 90} - \dfrac{3k + 27}{10k + 90} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{40k + 40 - (3k + 27) }{10k + 90} $ Distribute the negative sign: $z = \dfrac{40k + 40 - 3k - 27}{10k + 90}$ $z = \dfrac{37k + 13}{10k + 90}$